Annex 8: Price indeterminacy rules
There are cases where multiple solutions of the Market Coupling Problem have identical
block selections and identical welfares but different clearing prices. In the most frequent
cases, this arises when offer and demand curves overlap on a vertical segment. These
cases are called price indeterminacies. The aim of this appendix is to describe the rules
implemented in COSMOS to choose amongst these clearing prices.
P

UB
MCP*
LB

Q

Figure 1: Simple case of price indeterminacy

In a nutshell, COSMOS will pick the mid-point of the intersection, that is MCP* in the figure
above. However, in a realistic problem with several markets coupled over several hours,
this solution might be non-feasible. This would be the case for example if MCP* invalidates
the selection of block (i.e. the price acceptance of block orders are not compatible with
MCP*). In such a case, COSMOS will pick up the price which is closed to the mid point and
which respects all other price constraints.
This section explains in details how COSMOS selects prices in indeterminate cases1.

1.1.

Notations

Let’s note:
LBm,h: the lowest possible price in the market m on hour h for a defined net position Q*.
UBm,h: the highest possible price in the market m on hour h for a defined net position Q*.
MCPm,h: the (unrounded) Market Clearing Price of the market m on hour h.
The mid point of the intersection defined by [LBm,h, UBm,h] is equal to (UBm,h+LBm,h)/2.

1.2.

Mid point rule formulation for price determination

A potential feasible solution produced by the algorithm is definitively a feasible solution
once unique rounded prices satisfying all constraints can be defined for this solution.
In case of non-unique price solution, for a given hour h, the mid-point rule is defined
as the minimal square distance between MCPm,h and the distance to its “mid point”. In
case of several indeterminacies, the sum of these distances is considered. The midpoint price expression can be formulated with the following function

Published_Pricem,h: the price published by the Exchange in market m on
hour h
Precisionm: the precision of prices in market m
Pminm: the lower price boundary of market m
Pmaxm: the upper price boundary of market m

Note that market constraints are checked against these prices as well before being
published

1.4.

Summary

COSMOS lifts potential price indeterminacies by selecting the prices at the middle
of the feasible interval, taking into account the price constraints arising from
block selection and network configuration. Then Cosmos rounds and enforces
bounds on these prices before publication.